The invention relates to the field of satellite clusters and sparse antenna arrays. More particularly, the present invention relates to the deployment of satellites into a cluster operating as a sparse array antenna.
Communications satellites typically use electromagnetic waves in the radio frequency, microwave, and millimeter-wave range, from 1.0 MHz to 300 GHz, to communicate with terrestrial communication systems. The size of the antenna required is a function of the required gain or directionality and frequency used. Highly directional beams allow a single satellite to service a number of geographically dispersed users with a single frequency allocation. The highly directional beams enable significant frequency reuse to increase the overall system bandwidth. Attaining high gain or directionality in the radio frequency and low microwave frequency ranges from 10 MHz to 30 GHz can be useful for many communications and earth-sensing operations, but such high gain or directionality may require unacceptably large antenna apertures. To produce a 2.0 kilometer-diameter spot beam on the earth at a range of 1000 km at a frequency of 200 MHz, for example, requires that the satellite carry a one kilometer-diameter antenna. To get the same spot size from geosynchronous earth orbit will require an antenna with a 40.0 kilometer diameter.
The basic concept of using a cluster of satellites as a sparse aperture arrays is well known. A sparse array antenna is an array of antenna elements that are more than a wavelength apart. Sparse aperture antenna arrays can be used instead of a single large antenna. The arrays are particularly useful in applications serving geographically dispersed users because the beam directionality is typically more important than total signal gain. The resulting sparse array antenna must be large for high directionality while having many empty spaces within the resultant aperture. A large antenna is effectively emulated by coherently combining received signals from multiple small antennas. These multiple smaller antennas do not have to be physically connected. For example, a previously proposed orbital configuration consists of a single cluster ring of geostationary satellites. Gain pattern simulations of circular sparse aperture arrays show that kilometer-scale apertures composed of tens-to-thousands of individual dipole receiver elements, even with average inter-element spacing greater than ten wavelengths, can create highly directional beams useful for satellite communications.
A sparse array cluster of hundreds of satellites having a dynamic configuration extending over a kilometer in diameter is difficult to keep in formation. Orbiting cluster formations are disadvantageously disrupted due to natural perturbing forces such as solar radiation pressure, atmospheric drag, and earth gravity harmonics. Prior cluster formation disclosures have failed to teach how to provide suitable formation-keeping methods with tight tolerances for controlling the orbit of each satellite and for minimizing the total propellant expenditure for all the satellites to keep the satellites in formation. Prior cluster formation disclosures have also failed to teach how to provide viable cluster configurations for non-circular and non-geostationary orbits. These and other disadvantages are solved or reduced using the invention.
An object of the invention is to maintain an orbiting cluster of flying elements in a predetermined cluster formation as the cluster orbits the earth.
Yet another object of the invention is to maintain sparse array antenna elements in predetermined orbits and in a predetermined cluster formation with selected orbit parameters that minimize the use of propellant to maintain the cluster in formation and in the predetermined orbits.
A further object of the invention is to compute subsatellite subreference orbits from respective position and velocity vectors of the subsatellites, which vectors are computed from position and velocity vectors of a center satellite within the cluster.
Still another object of the invention is to compute thrust vectors from the computed subsatellite subreference orbits for rigidly maintaining the subsatellites the cluster formation.
Another object of the invention is to compute subsatellite subreference orbits from respective position and velocity vectors of the subsatellites, which vectors are computed from position and velocity vectors of a center satellite within the cluster, which center satellite has an inclined eccentric frozen orbit.
The method is primarily directed to space missions where the payload function is distributed among several flying elements arranged in a cluster having a center point traveling through a reference orbit where the elements fly in a rigid formation requiring a relatively small amount of xcex94V thrust to maintain the cluster in the rigid formation while traveling along the reference orbit. The arbitrary flying elements can be small microsatellites or nanosatellites configured in the cluster formation as an on-orbit sparse aperture array with an overall dimension from tens-of-meters to thousands-of-kilometers. To create a cluster of satellites, orbital parameters are chosen so that each satellite occupies a node in an arbitrary spatial pattern and so that the satellite formation undergoes a cyclic motion about the center point of the cluster. The cyclic motion is preferably rotational where the satellites revolve around the center point. The formation is rigidly maintained for the duration of the mission using microthrusting. The cyclic motion of the satellite formation enables the formation to persist for several revolutions without microthrusting maneuvering. Orbital mechanics define and maintain the planar rigid formation of unconnected satellites acting as individual antenna elements within the cluster of satellites preferably comprising a mother-ship center satellite and a plurality of subsatellites in a two-dimensional suborbit plane. The subsatellites preferably suborbit around the center satellite as the center satellite orbits the earth through the reference orbit that may be a low earth orbit (LEO) as the subsatellites orbit the earth through respective subreference orbits. The method allows for the maintenance and formation-keeping of the orbiting two-dimensional sparse aperture array having the free-flying center satellite and the suborbiting subsatellites that remain spatially fixed with respect to each other within a fraction of the average inter-element spacing to eliminate the possibility of inter-satellite collisions while providing a slowly-changing antenna side lobe distribution.
The sparse array antenna has a reference orbit along which the center satellite travels and around which the other individual subsatellites suborbit. The cluster of subsatellites is disposed in a cluster suborbit plane having a normal that is inclined, for example 60xc2x0, from the normal of the reference orbit in a direction towards the instantaneous nadir. A first orbital parameter that is initially chosen is the semimajor axis. The semimajor axis of the subreference orbits for all of the subsatellites is equal to the semimajor axis of the reference orbit of the center satellite, to the first order, so that the orbital periods are identical. In a cluster reference frame, the subsatellites suborbit about the center satellite at the center of the cluster once per orbit around the earth. Each subsatellite has a respective subreference orbit plane that intersects along a respective intersection line with the reference orbit. The intersection line intersects the reference orbit at two intersection points, that is, the (1/2) xcfx80 and (3/2) xcfx80 intersection points of the reference orbit thereby defining xcfx80 and 2xcfx80 alignment points of the reference orbit. The other five orbital parameters necessary for determining the subreference orbit of any one of the subsatellites within the cluster can be determined by realizing that at the xcfx80 and 2xcfx80 alignment points along the subreference orbit, the subsatellite velocity vector is aligned in parallel to the center satellite velocity vector, but having a different magnitude. As such, the radial position and velocity vectors of each of the subsatellites can be computed from the radial position and velocity vector of the center satellite. The other five orbital parameters, including eccentricity, inclination, right ascension of the ascending node, argument of the perigee, and mean anomaly, are uniquely determined for any particular subsatellite from the respective position and velocity vectors of the respective subsatellite. This method is applicable for reference orbits having arbitrary choices of inclination and eccentricity.
The configuration of the formation is maintained as the cluster orbits the earth. When the cluster suborbit plane is inclined relative to the reference orbit plane, for example, at a 60xc2x0 suborbit plane angle, there is no radial motion of the subsatellites within the cluster suborbit plane relative to the center satellite, and the suborbits are circular so that the cluster appears to rotate as a rigid body with each subsatellite traveling in a circle around the center satellite at the same radial distance. When the suborbit plane angle is different than 60xc2x0, the radial distances between the center point and the subsatellites cycle between maximums and minimums twice per orbit around the earth, and, the suborbits are elliptical and the cluster appears as a non-rigid elliptical body, with the subsatellites changing relative radial positions with respect to the center satellite. In all cases of suborbit plane angle, the shape of the formation is maintained and all of the subsatellites return to an initial position once per revolution around the earth. An arbitrary cluster distribution of satellites in the cluster suborbit plane can be maintained, and this cluster suborbit plane will rotate about the earth such that the suborbit plane normal is always pointing towards the earth, ninety degrees minus the suborbit plane angle, for example 30xc2x0 degrees in the case of a 60xc2x0 suborbit plane angle, above or below the center reference orbit plane.
The orbit maintenance and formation keeping is based on the selection of a frozen reference orbit and multiple thruster microcorrections for each subsatellite per orbit. Use of a frozen reference orbit minimizes the variations in eccentricity and argument of perigee caused by higher-order gravitational harmonics created by variations in geopotential gravity fields. The microcorrections occur along in-track and cross-track directions and are computed using an auto-feedback controller based on instantaneous relative position and velocity deviations that are derived from the position and velocity of the center satellite. With this method, formation-keeping propulsion requirements are reduced using conventional on-orbit thrusters even for multi-kilometer diameter clusters in a low earth orbit (LEO). The frozen orbit selection and multiple micro-corrections per orbit enable formation keeping with minimum propellant usage without restriction as to the size of the sparse array.
Use of an inclined planar cluster of satellites as a distributed sparse array antenna with coherent signal combining can create custom beam patterns for radio frequency and microwave communications applications. The cluster orbit can have arbitrary inclination and eccentricity. The use of multiple microcorrections per orbit provides for rigid formation keeping during a mission. The method enables the creation of extremely narrow or user-defined beamwidths at VHF, UHF, and microwave frequencies without requiring kilometer size antennas on the satellite. Coherent signal combining allows for the simultaneous generation of multiple spot beams. The coherent signal combining allows for orders-of-magnitude more frequency reuse of the VHF through microwave spectrum for space communications. The method provides for a free-flying nongeosynchronous sparse aperture array with coherent signal combining that can operate at any orbit altitude. The individual antenna subsatellites may be dispersed at various radii and azimuth angles within the cluster suborbit plane to fill a given aperture with a predetermined planar density distribution. The dispersion enables higher densities near the cluster center for improved aperture efficiency and effectively enables a tapered illumination profile. The dispersion also allows for custom density distributions for generating non-circular beam footprints. These and other advantages will become more apparent from the following detailed description of the preferred embodiment.